Maxima is a symbolic math software that resembles Maple. I have been able to play around with and I am very happy with it. Thus far I have managed to do the following:

(%i36) f(x,y):=4*(y^4)+exp(x)-(x^3)/6;

(%o36) f(x,y):=4*y^4+exp(x)+(-x^3)/6

(%i37) hessian(f(x,y),[x,y]);

(%o37) matrix([%e^x-x,0],[0,48*y^2])

That is: define a function of x and y, calculate its hessian matrix... But I have not been able to calculate the gradient... Has anyone played with this? I have googled all over the place and have not been able to find the answer to this question...

so that: grad(f(x,y)) gives: exp(x)-(x²/2) , 16y³...

Thanks